Abstract
We prove uniqueness for extended real-valued lower semicontinuous viscosity solutions of the Bellman equation forL ∞-control problems. This result is then used to prove uniqueness for lsc solutions of Hamilton-Jacobi equations of the form −u t +H(t, x, u, −Du)=0, whereH(t, x, r, p) is convex inp. The remaining assumptions onH in the variablesr andp extend the currently known results.
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Communicated by F. H. Clarke
Supported in part by Grant DMS-9300805 from the National Science Foundation.
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Barron, E.N., Liu, W. Semicontinuous solutions for Hamilton-Jacobi equations and theL ∞control problem. Appl Math Optim 34, 325–360 (1996). https://doi.org/10.1007/BF01182629
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DOI: https://doi.org/10.1007/BF01182629